A sample of isotropic material is subjected to a compressive stress o and is confined so...
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A sample of isotropic material is subjected to a compressive stress o and is confined so that it cannot deform in either the x- or y-directions, as shown in Fig. (a) Do stresses occur in the material in the x- and y-directions? If so, obtain equations for o, and for oy, each as functions of only o and the elastic constant v for the material. (b) Determine the stiffness E' = /8, in the direction of the applied stress o in terms of only the elastic constants E and v for the material. Is E' equal to the elastic modulus E as obtained from a uniaxial test? Why or why not? (c) What happens if Poisson's ratio for the material approaches 0.5? material Z H rigid die A sample of isotropic material is subjected to a compressive stress o and is confined so that it cannot deform in either the x- or y-directions, as shown in Fig. (a) Do stresses occur in the material in the x- and y-directions? If so, obtain equations for o, and for oy, each as functions of only o and the elastic constant v for the material. (b) Determine the stiffness E' = /8, in the direction of the applied stress o in terms of only the elastic constants E and v for the material. Is E' equal to the elastic modulus E as obtained from a uniaxial test? Why or why not? (c) What happens if Poisson's ratio for the material approaches 0.5? material Z H rigid die
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